Hi CO,
Primarily by breaking down the problem and solving it one part at a time.
Having a general knowledge of the architecture of a common power supply helped me focus on the system's functional parts that are most likely to be affected. For example, when I was switching it on the displayed I/V was fluctuating randomly, occasionally displaying values outside the specs of this power supply. This implies that there is something wrong in the ADC or power section.
I could further break down the problem using the full schematics of the unit found online. Then you can probe individual subcircuits (starting with voltages is helpful) and with your electronics knowledge make a call if they are faulty. For example, an inverting op-amp topology was outputting its rail voltage while R1=R2. That's not right, and it turned out one of the resistors was open-circuit leading to no feedback.
Doing some research online I read that the analogue optocouplers are quite sensitive and prone to failure. I checked the voltage across the LED and it was 2.4V when you can see in their datasheet that the typical value is 1.4V. So these were open-circuit.
The heart of the ADC section is current-based, so probing with a voltmeter gave little information. If I suspected something was faulty, I made a call to replace it as this is easier than running more extensive diagnostics. There was a buffer op-amp outputting something different to its input while driving a reasonably high impedance, so that op-amp was faulty.
When the supply started working again I did a short-circuit test and from CV I was expecting it to switch to CC. It displayed 'Unreg', suggesting the CC/CV comparator was faulty and gave the wrong signals to the main processor.
In the end everything worked OK but it still displayed ERROR. I was about to just leave it as it is, thinking that the fault was around the RS232/GPIB section which I don't need. I probed one of the optocouplers as I had to replace a similar one and voila, it was faulty.
Overall I was lucky that the main processor (integral part of the ADC) was not damaged, I would not be able to replace that easily.
This would have not been a commercially viable repair, a lot of time and money was spent on finding and replacing components. But it is a good power supply to have on the bench.